Can an imported .STL file be broken down into individual parts (rigged) and animated in Blender?
Yes it should be possible, since importing means to convert it into Blender internal format. You can use all tools provided by Blender to work on you model. 

It could be that you need to split the window and the window frame into two objects. 
In Edit Mode select the part of the mesh you want so separate into to another object and press P this opens the Separate popup and choose Selection.